function [J grad] = nnCostFunction(nn_params, ...
                                   input_layer_size, ...
                                   hidden_layer_size, ...
                                   num_labels, ...
                                   X, y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
%   X, y, lambda) computes the cost and gradient of the neural network. The
%   parameters for the neural network are "unrolled" into the vector
%   nn_params and need to be converted back into the weight matrices. 
% 
%   The returned parameter grad should be a "unrolled" vector of the
%   partial derivatives of the neural network.
%

% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
                 hidden_layer_size, (input_layer_size + 1));

Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
                 num_labels, (hidden_layer_size + 1));

% Setup some useful variables
m = size(X, 1);

% You need to return the following variables correctly 
J = 0;
Theta1_grad = zeros(size(Theta1));
Theta2_grad = zeros(size(Theta2));

% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
%               following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
%         variable J. After implementing Part 1, you can verify that your
%         cost function computation is correct by verifying the cost
%         computed in ex4.m

% Adding first columns
X = [ones(m,1) X];

a1=X;
	
% Compute activation of hidden layer
z2 = X*Theta1';
a2 =[ones(m,1) sigmoid(z2)] ;

% Compute output layer
z3 = a2*Theta2';
a3= sigmoid(z3);

y_temp = eye( num_labels );
yvector = y_temp( y, : );

su = sum(sum(yvector .* log(a3) + (1 - yvector) .* log( 1 - a3)));
J = -su/m + lambda/(2*m)*(sum(sumsq(Theta1(:,2:end))) + sum(sumsq(Theta2(:,2:end))));

%
% Part 2: Implement the backpropagation algorithm to compute the gradients
%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
%         Theta2_grad, respectively. After implementing Part 2, you can check
%         that your implementation is correct by running checkNNGradients
%
%         Note: The vector y passed into the function is a vector of labels
%               containing values from 1..K. You need to map this vector into a 
%               binary vector of 1's and 0's to be used with the neural network
%               cost function.
%
%         Hint: We recommend implementing backpropagation using a for-loop
%               over the training examples if you are implementing it for the 
%               first time.
%
% Back Propagation

%for t=1:m	
	% Compute activation of hidden layer
%	z2 = X*Theta1';
%	a2 =[ones(m,1) sigmoid(z2)] ;

	% Compute output layer
%	z3 = a2*Theta2';
%	a3= sigmoid(z3);
	
	% Error at output layer
%	delta3 = a3 - y;
	
	% Error at hidden layer
%	delta2 = ( delta3 * Theta2) .* ( sigmoidGradient( a2));
 %	delta2 = delta2( :,2 : end );
    	
 %   	Theta1_grad += delta2 '* a1;
%	Theta2_grad += delta3 '* a2;
%endfor;


for t = 1 : m

	a1 = X( t, : );
	
	% Compute activation node at hidden
	z2 = a1 * Theta1';
	a2 = sigmoid(z2);
	a2 = [ones(size(a2,1),1),a2];
	z2 = [ones(size(z2,1),1),z2];
	
	% Compute activation node at output layer
	z3 = Theta2 * a2';
	a3 = sigmoid(z3);
	
	%Computer error at output layer
	delta3 = a3 - yvector'( :, t );
	
	% Compute error at hidden layer
	delta2 = ( Theta2' * delta3 ) .* ( sigmoidGradient( z2 ) )';
	delta2 = delta2( 2 : end );
	
	% Update theta
	Theta1_grad = Theta1_grad + delta2 * a1;
	Theta2_grad = Theta2_grad + delta3 * a2;
endfor

% Update Theta Gradient
Theta1_grad = Theta1_grad ./ m;
Theta2_grad = Theta2_grad ./ m;

% Part 3: Implement regularization with the cost function and gradients.
%
%         Hint: You can implement this around the code for
%               backpropagation. That is, you can compute the gradients for
%               the regularization separately and then add them to Theta1_grad
%               and Theta2_grad from Part 2.
%

% Add Reglarization
Theta1_grad(:,2:end) = Theta1_grad(:,2:end) + lambda/m*Theta1(:,2:end);
Theta2_grad(:,2:end) = Theta2_grad(:,2:end) + lambda/m*Theta2(:,2:end);

% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];

end
